14-10] METEOROLOGICAL EFFECTS AT MICROWAVE FREQUENCIES 761 



This presumes a given size distribution of drops based on the work of Laws 

 and Parsons® and indicates n varying with the 1.6 power of rainfall rate for 

 this one specific case. There is some evidence to indicate that this figure 

 represents a common rainfall condition. The symbol ^ is a proportionality 

 constant. 



3. The factor \K\'^ is about five times larger for water than for ice. 

 This results in much stronger returns from rain than from dry snow, for 

 equivalent masses. However, as ice particles fall through warmer layers 

 and melting water forms on their surface, they very rapidly take on the \K\^ 

 value of water. Particularly in the case of hail falling through the melting 

 zone, very high values of back-scattering occur because of the large diam- 

 eters (Z)) involved. This gives rise to the so called bright band effect 

 mentioned in Sec. 4-16. 



Another interesting facet of meteorological scatterers is the effect of shape 

 on back-scattering. Equation 14-14 is based on spherical hydrometeors. As 

 these particles become elongated or flattened out, the value of n increases, 

 assuming a random orientation of the spheroids. As a result, snow or ice 

 particles having distorted shapes often give strong returns as they fall 

 through the melting band, before they form into more uniform rain droplets. 



Rain droplets, if large enough in size, flatten as they fall, resulting 

 in somewhat greater target returns for horizontally polarized energy 

 impinging upon them than from vertically polarized energy. 



Meteorological Attenuators. Weather hydrometeors are not only 

 to be considered from the standpoint of reflective scatterers, but also as 

 attenuators of the radar signal when they happen to lie between the radar 

 antenna and a desired target. Part of this attenuation is caused by diffusion 

 and part by absorption of the microwave energy. This attenuation is 

 usually designated round trip attenuation (7) and is in terms of decibels per 

 unit distance of attenuating media. 7 can be expressed as a function 



7=/(X,M) (14-16) 



where M is in terms of water density, gm/m^ In the case of rainfall 



7 = AB^ (14-17) 



where R is the equivalent rainfall rate in mm hr~^ and ^ is a parameter that 

 varies with wavelength and temperature. For the case of rain, the exponen- 

 tial b is essentially unity for wavelengths of 10 cm and longer and increases 

 to about 1.3 at X = 3 cm. 



As was the case with the scattering coefficient «, attenuation 7 increases 

 rapidly with frequency and is much greater for rain than for snow, fog, or 



*J. O. Laws and D. A. Parsons, "The Relation of Raindrop Size to Intensity," Trans. Am. 

 Geophys. Union 24, part 2, 1943. 



